TY - JOUR

T1 - STRATIFICATIONS OF THE RAY SPACE OF A TROPICAL QUADRATIC FORM BY CAUCHY–SCHWARTZ FUNCTIONS

AU - Izhakian, Zur

AU - Knebusch, Manfred

N1 - Publisher Copyright:
© 2022, International Linear Algebra Society. All rights reserved.

PY - 2022

Y1 - 2022

N2 - Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlying structure of ‘supertropical trigonometry’ and thereby a version of convex geometry which is compatible with quasilinearity. In this theory, the traditional Cauchy–Schwarz inequality is replaced by the CS-ratio, which gives rise to special characteristic functions, called CS-functions. These functions partite the ray space Ray(V) into convex sets and establish the main tool for analyzing varieties of quasilinear stars in Ray(V). They provide stratifications of Ray(V) and, therefore, a finer convex analysis that helps better understand geometric properties.

AB - Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlying structure of ‘supertropical trigonometry’ and thereby a version of convex geometry which is compatible with quasilinearity. In this theory, the traditional Cauchy–Schwarz inequality is replaced by the CS-ratio, which gives rise to special characteristic functions, called CS-functions. These functions partite the ray space Ray(V) into convex sets and establish the main tool for analyzing varieties of quasilinear stars in Ray(V). They provide stratifications of Ray(V) and, therefore, a finer convex analysis that helps better understand geometric properties.

KW - Bilinear forms

KW - Cauchy–Schwarz functions

KW - Cauchy–Schwarz ratio

KW - Convex sets

KW - Quadratic forms

KW - Quadratic pairs

KW - Quasilinear sets

KW - Ray spaces

KW - Stratifications

KW - Supertropical algebra

KW - Supertropical modules

UR - http://www.scopus.com/inward/record.url?scp=85139094437&partnerID=8YFLogxK

U2 - 10.13001/ela.2022.6493

DO - 10.13001/ela.2022.6493

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AN - SCOPUS:85139094437

SN - 1537-9582

VL - 38

SP - 531

EP - 558

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -